PRISM: PRIor from corpus Statistics for topic Modeling

Tal Ishon; Yoav Goldberg; Uri Shaham

cs.LGMar 31, 2026

PRISM: PRIor from corpus Statistics for topic Modeling

Authors: Tal Ishon, Yoav Goldberg, Uri Shaham

Organizations: Department of Computer Science, Bar Ilan University

Abstract

Topic modeling seeks to uncover latent semantic structure in text, with LDA providing a foundational probabilistic framework. While recent methods often incorporate external knowledge (e.g., pre-trained embeddings), such reliance limits applicability in emerging or underexplored domains. We introduce PRISM, a corpus-intrinsic method that derives a Dirichlet parameter from word co-occurrence statistics to initialize LDA without altering its generative process. Experiments on text and single cell RNA-seq data show that PRISM improves topic coherence and interpretability, rivaling models that rely on external knowledge. These results underscore the value of corpus-driven initialization for topic modeling in resource-constrained settings. Code is available at: https://github.com/shaham-lab/PRISM.

Figures & tables

Figure 1: PRISM overview. From corpus $\mathcal{D}$ , we build a second-order word-similarity graph (PPMI + cosine), obtain diffusion-map embeddings $v_{i}$ , softly cluster them into $K$ topics, and estimate a data-driven topic–word Dirichlet prior $\hat{\boldsymbol{\beta}}$ for LDA. The lower panel shows the standard LDA graphical model; PRISM replaces the symmetric $\boldsymbol{\beta}$ with $\hat{\boldsymbol{\beta}}$ while leaving the generative process unchanged.

MODELS	20NewsGroup	BBC	M10	DBLP	TrumpTweets
ProdLDA	.4561 (.0165)	.4556 (.0681)	.2232 (.0322)	.2528 (.0638)	.2759 (.0722)
NeuralLDA	.2533 (.0518)	.3259 (.0060)	.1194 (.0211)	.1667 (.0667)	.1296 (.0414)
LDA	.1472 (.0202)	.1333 (.3615)	.1139 (.4885)	.0833 (.9211)	.1611 (.5625)
ETM	.3422 (.0301)	.4592 (.0726)	.0889 (.3713)	.1194 (.6224)	.1130 (.9177)
NMF	.1411 (.0196)	.0630 (.3148)	.0010 (.8161)	.0010 (.8161)	.2426 (.3977)
BERTopic	.3811 (.0452)	.5537 (.0092)	.4907 (.0227)	.3584 (.0118)	.3139 (.0103)

Table 2: Word Intrusion Detection accuracy across five datasets (mean (std) over three topic settings). Best is bold , second-best is underlined ; † indicates PRISM outperforms MALLET.

Panel of Figure 2 — Figure 2: Top-10 words per topic on the BBC dataset with $K=5$ . Each column is a distinct topic. Colors denote manually interpreted categories ( politics politics politics politics politics politics politics politics politics politics politics politics politics politics politics politics politics , entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment , business business business business business business business business business business business business business business business business business , sports sports sports sports sports sports sports sports sports sports sports sports sports sports sports sports sports , technology technology technology technology technology technology technology technology technology technology technology technology technology technology technology technology technology ); lighter shades indicate weaker relevance and white indicates no clear association. Panels: ( 2(a) ) BERTopic, ( 2(b) ) ProdLDA, ( 2(c) ) PRISM.

Models	BreastCancer			PBMC3k			Zeisel brain
Models	Coherence	Coverage	Strength	Coherence	Coverage	Strength	Coherence	Coverage	Strength
cNMF	0.2695	0.0	—	0.3867	0.8	10.2447	0.6306	0.8	4.1679
scHPF	0.2423	0.2	1.4056	0.1694	0.6	6.0057	0.4049	0.6	3.4919
ProdLDA	0.0956	0.0	—	0.0091	0.0	—	0.0273	0.0	—
NMF	0.0918	0.0	—	0.0068	0.0	—	0.0395	0.0	—
MALLET	0.2471	0.0	—	0.2952	0.8	9.0515	0.5541	0.8	2.2903

Table 3: Gene-set quality metrics for biological datasets. Each entry is the mean over 10 runs with

K=5

. Coherence = mean within-set Spearman correlation; Coverage = fraction of pathway members recovered (averaged over significant pathways); Strength =

-\log_{10}(q)

(FDR-adjusted). “—” indicates no significant pathway enrichments (

q\!\geq\!0.05

). Best scores are bold ; second-best are underlined ;

\dagger

indicates PRISM significantly outperforms MALLET for that metric (test details in the Supplement).

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	#Docs	Vocab	Avg. Len.	#Labels	$K$
20NewsGroup	16,309	1,612	48.0	20	20, 25, 50
BBC	2,225	2,949	12.1	5	5, 10, 15
M10	8,355	1,696	5.9	10	10, 15, 20
DBLP	54,595	1,513	5.4	4	4, 10, 15
TrumpTweets	18,239	1,988	9.0	–	10, 15, 20

Appendix

Table 4: Dataset statistics. Avg. Len. denotes average document length in tokens;

K

lists the topic counts used.

Figure 5: Illustration of the Word Intrusion Detection (WID) framework. A large language model is prompted to identify the word that does not belong in a list of top topic words (a.k.a. the intruder). The prompt shown here is illustrative; actual prompts used in our experiments follow a more structured format.

Figure 6: Prompt template for the Word Intrusion Detection (WID) task, with instructions, two illustrative examples, and a structured response format. The input variable numbered_word_list is inserted at evaluation time to test different word sets.

Asset	License / Terms
Software / libraries
OCTIS	MIT License 9 9 9 https://github.com/MIND-Lab/OCTIS/blob/master/LICENSE
Gensim	LGPL v2.1 (or later) 10 10 10 https://github.com/RaRe-Technologies/gensim/blob/develop/LICENSE
MALLET	Apache License 2.0 11 11 11 http://mallet.cs.umass.edu/ (see LICENSE in the distribution)
BERTopic	MIT License 12 12 12 https://github.com/MaartenGr/BERTopic/blob/master/LICENSE
Contextual-Top2Vec (Top2Vec)	BSD 3-Clause 13 13 13 https://github.com/ddangelov/Top2Vec/blob/master/LICENSE

Appendix

Table 5: Licenses / terms for third-party software and assets.

Panel of Figure 7 — Figure 7: Top-10 words per topic on the BBC dataset with $K=5$ . Each column is a distinct topic. Colors in the panels denote manually interpreted categories ( politics politics politics politics politics politics politics politics politics politics politics politics politics politics politics politics politics , entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment entertainment , business business business business business business business business business business business business business business business business business , sports sports sports sports sports sports sports sports sports sports sports sports sports sports sports sports sports , and technology technology technology technology technology technology technology technology technology technology technology technology technology technology technology technology technology ); lighter shades indicate weaker relevance and white indicates no clear association. Panels: ( 7(a) ) MALLET, ( 8(b) ) PRISM.

Panel of Figure 8 — Figure 8: Heatmaps on the BBC dataset with $K=5$ . Each column corresponds to a topic. Each column corresponds to a topic and each row to a top-ranked word (from the union of topics). Cell colors encode the topic-word relevance (i.e., $\phi_{k,w}$ , shown on a log scale in the colorbar): lighter/yellow shades indicate higher probability mass, whereas darker/purple shades indicate lower probability. Panels: ( 8(a) ) FASTopic, ( 8(b) ) PRISM, ( 8(c) ) ProdLDA.

Panel of Figure 9 — Figure 9: Heatmaps on the M10 dataset with $K=10$ . Each column corresponds to a topic and each row to a top-ranked word (from the union of topics). Cell colors encode topic–word relevance (i.e., $\phi_{k,w}$ , shown on a log scale in the colorbar): lighter/yellow shades indicate higher probability mass, whereas darker/purple shades indicate lower probability. Panels: ( 9(a) ) BERTopic, ( 9(b) ) PRISM, ( 9(c) ) FASTopic.

MODELS	20NewsGroup	BBC	M10	DBLP	TrumpTweets
GloVe Embed	.5590 (.0480)	.5778 (.0072)	.3672 (.0492)	.2844 (.0376)	.2733 (.0618)
Random Prior	.5277 (.0494)	.5467 (.0091)	.3161 (.0547)	.2506 (.0448)	.2328 (.0627)
No SOC (PPMI $\rightarrow$ DM)	.5637 (.0492)	.5233 (.0145)	.3633 (.0577)	.2750 (.0467)	.2744 (.0687)
SVD in place of DM	.5543 (.0514)	.5533 (.0132)	.3589 (.0615)	.3133 (.0455)	.2411 (.0714)
PRISM (reference)	.6099 (.0124)	.6201 (.0281)	.3921 (.0176)	.3408 (.0512)	.3057 (.0131)

Appendix

Table 7: Word Intrusion Detection (WID) accuracy for ablations across datasets. Each entry is mean accuracy (std) over 10 runs. Ablations: GloVe Embed (GloVe term embeddings

\rightarrow

GMM; MoM to Dirichlet prior), Random Prior (random vector prior), No SOC (PPMI

\rightarrow

DM; cosine-similarity step removed), SVD in place of DM (SOC-PPMI

\rightarrow

SVD

\rightarrow

GMM).

MODELS	20NewsGroup	BBC	M10	DBLP	TrumpTweets
PRISM (w=2)	.5850 (.0180)	.5600 (.0300)	.3780 (.0220)	.3180 (.0500)	.2870 (.0180)
PRISM (w=5)	.5975 (.0150)	.5950 (.0260)	.3860 (.0190)	.3310 (.0480)	.2980 (.0150)
PRISM (w=10)	.6068 (.0130)	.6150 (.0240)	.3910 (.0180)	.3385 (.0520)	.2996 (.0104)
MALLET	.5681 (.0206)	.4689 (.0412)	.3711 (.0406)	.3031 (.0554)	.2697 (.0302)
PRISM (doc-level)	.6099 † (.0124)	.6201 † (.0281)	.3921 † (.0176)	.3408 † (.0512)	.3057 † (.0131)

Appendix

Table 9: Ablation on PPMI context window size for Word Intrusion Detection (WID) accuracy (mean (std) over three topic settings). Best is bold , second-best is underlined .

Model	Time (dominant)	Space (dominant)
BoW topic/factor models
LDA	$O(\mathrm{nnz}(X)\,K)+O(\|V\|K)$	$O(\mathrm{nnz}(X)+NK+\|V\|K)$
NMF	$O(\mathrm{nnz}(X)\,K)$	$O(\mathrm{nnz}(X)+NK+\|V\|K)$
ProdLDA	$O(\mathrm{nnz}(X)\,K)+O(\|\Theta\|)$	$O(\mathrm{nnz}(X)+NK+\|V\|K+\|\Theta\|)$
ETM	$O(\mathrm{nnz}(X)\,K)+O(\|V\|K)$	$O(\mathrm{nnz}(X)+NK+\|V\|K)$
CTM	$O(\mathrm{nnz}(X)\,K)+O(\|\Theta\|)$	$O(\mathrm{nnz}(X)+NK+\|V\|K+\|\Theta\|)$

Appendix

Table 10: Dominant time and space complexities.

Model	20NewsGroup	BBC	M10	DBLP	TrumpTweets
MALLET	38.24 (6.81)	32.65 (0.58)	31.11 (0.23)	32.26 (1.69)	31.07 (0.61)
PRISM	46.67 (12.42)	38.08 (2.10)	39.56 (5.29)	42.67 (4.04)	34.67 (2.52)
BERTopic	668.14 (7.50)	130.06 (5.46)	102.30 (21.63)	2005.01 (51.50)	625.45 (42.38)

Appendix

Table 11: Wall-clock runtime in seconds (mean (std) over three runs).

Models	BreastCancer	pbmc3k	zeisel_brain
cNMF	.8000 (.0505)	.9021 (.0401)	.9330 (.0172)
scHPF	.7712 (.0240)	.8326 (.0235)	.8980 (.0658)
NMF	.7880 (.0331)	.6590 (.0141)	.6670 (.0435)
ProdLDA	.7600 (.0469)	.4950 (.1862)	.5950 (.0282)
MALLET	.7920 (.0352)	.8392 (.0276)	.8920 (.0268)
PRISM	.8320 † (.0171)	.8997 † (.0167)	.9350 † (.0206)

Appendix

Table 12: LLM-based evaluation scores (mean and std over 10 runs) across biological datasets.

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In this paper, we propose Precision-Informed Semantic Modeling (PRISM), a structured topic modeling framework combining the benefits of rich representations captured by LLMs with the low cost and interpretability of latent semantic clustering methods. PRISM fine-tunes a sentence encoding model using a sparse set of LLM- provided labels on samples drawn from some corpus of interest. We segment this embedding space with thresholded clustering, yielding clusters that separate closely related topics within some narrow domain. Across multiple corpora, PRISM improves topic separability over state-of-the-art local topic models and even over clustering on large, frontier embedding models while requiring only a small number of LLM queries to train. This work contributes to several research streams by providing (i) a student-teacher pipeline to distill sparse LLM supervision into a lightweight model for topic discovery; (ii) an analysis of the efficacy of sampling strategies to improve local geometry for cluster separability; and (iii) an effective approach for web-scale text analysis, enabling researchers and practitioners to track nuanced claims and subtopics online with an interpretable, locally deployable framework.

Abstract

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